高阶涡旋系统中的可调多带几何与分数相位
Tunable Multiband Geometry and Fractional Phases in Higher Vortexable Systems
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中文总结 AI 辅助
该研究以高阶涡旋莫尔系统为对象，通过精确对角化方法，揭示零磁场下多带结构中由量子几何调谐的多类拓扑相，确立其为探索几何驱动多带拓扑相的可调平台。
中文摘要 AI 辅助
高阶涡旋性通常被视为获取具有类朗道能级量子几何的拓扑平带的途径，本文强调互补视角：它提供了一种可调多带结构，其中波函数几何可连续变化，而带色散、简并度和拓扑保持固定。我们对分数填充的高阶涡旋莫尔系统中的多体相进行系统精确对角化研究，保留完整平带希尔伯特空间而非投影到单带。多带处理揭示了零磁场下的一系列阿贝尔和非阿贝尔相，包括整数和分数激子绝缘体、阿贝尔分数量子霍尔绝缘体、Moore-Read态与Read-Rezayi态。在固定填充下，不同相仅通过波函数几何变化驱动的相变或交叉过渡相连，凸显量子几何本身是竞争拓扑态间的直接调谐参数。在与Moore-Read和Read-Rezayi态相关的填充下，计算表明带间混合改变了最优量子几何区域，但在屏蔽库仑相互作用下并未抑制非阿贝尔拓扑序。我们的结果确立了高阶涡旋莫尔带作为零磁场下探索几何驱动多带拓扑相的可调平台。
英文摘要
Higher vortexability is often viewed as a route to topological flat bands with higher-Landau-level-like quantum geometry. Here we emphasize a complementary perspective: it provides a tunable multiband structure in which wave function geometry can be varied continuously while the band dispersion, degeneracy, and topology remain fixed. We perform systematic exact-diagonalization studies of many-body phases in fractionally filled higher vortexable moiré systems, retaining the full flat-band Hilbert space rather than projecting onto a single band. The multiband treatment reveals a cascade of Abelian and non-Abelian phases at zero magnetic field, including integer and fractional exciton insulators, Abelian fractional Chern insulators, Moore-Read and Read-Rezayi states. At fixed filling, different phases are connected through transitions or crossovers driven solely by changes in wave function geometry, highlighting quantum geometry itself as a direct tuning parameter between competing topological states. At fillings associated with Moore-Read and Read-Rezayi states, our calculations show that interband mixing shifts the optimal quantum geometry regime without suppressing non-Abelian topological order under screened Coulomb interaction. Our results establish higher vortexable moiré bands as a tunable platform for exploring geometry-driven multiband topological phases at zero magnetic field.
